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Quantum mechanical entanglement is a resource for quantum computation, quantum teleportation, and quantum cryptography. The ability to quantify this resource correctly has thus become of great interest to those working in the field of…
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global…
Efficiently detecting entanglement based on measurable quantities is a basic problem for quantum information processing. Recently, the measurable quantities called partial-transpose (PT)-moments have been proposed to detect and characterize…
Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…
The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite…
Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the positive partial transposition…
The separability detecting problem of mixed states is one of the fundamental problems in quantum information theory. In the last 20 years, almost all methods are based on the sufficient or necessary conditions for entanglement. However, in…
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state…
The quantification of quantum entanglement is a central issue in quantum information theory. Recently, Gao \emph{et al}. ( \href{http://dx.doi.org/10.1103/PhysRevLett.112.180501}{Phys. Rev. Lett. \textbf{112}, 180501 (2014)}) pointed out…
We study fidelity and fidelity susceptibility by addition of entanglement of entropy in the one-dimensional quantum compass model in a transverse magnetic field numerically. The whole four recognized gapped regions in the ground state phase…
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the…
Characterizing quantum phase transitions through quantum correlations has been deeply developed for a long time, while the connections between dynamical phase transitions (DPTs) and quantum entanglement is not yet well understood. In this…
Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
We analyse the problem of distillation of entanglement of mixed states in higher dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a criterion of…
The certification of entanglement in multipartite scenarios is crucial for the advancement of quantum technologies, particularly for the realization of large-scale quantum networks. Here, we introduce a method to certify the structure of…